Removable tools are often carried in collets or chucks coupled to rotary machine tools, or driving spindles thereof by floating holders which permit compensation for misalignments between the machine spindle, to which, for example, the tool is secured and a hole into which it is to enter. Such floating holders customarily have two slider guides, respectively offset by 90 degrees, to permit compensation between the axis of the drive spindle and the axis of a bore, into which the tool is to enter. Such floating holders are not provided to set an axial offset with respect to a fixed amount, or to compensate for actual offsets and reduce them to a value of 0.